Finite Element Method (FEM) in Graphene Analysis

Methods based on atomic behavior, such as molecular dynamics (MD) simulations, are highly accurate for modeling single-layer graphene sheets. However, their high computational cost limits their use to only small-sized systems. This research addresses this limitation by developing a new atomic-scale finite element method (AFEM) based on the Tersoff-Brenner potential to analyze the mechanical properties of graphene. The proposed AFEM method's efficiency and accuracy were demonstrated through a numerical example of a graphene sheet. When compared to MD simulation results, the new method showed very high accuracy. Additionally, its simulation speed was found to be approximately ۱۰۰ times faster than that of the MD method. This study also investigated the influence of effective factors on simulation speed, such as the initial non-equilibrium bond length and the number of atoms. The AFEM was further developed to incorporate periodic boundary conditions, as these had not been previously considered for nanostructures using this method. The results showed that AFEM modeling without periodic boundary conditions produced results that were very different from those of MD simulations.

کلیدواژه ها:

Finite Element ، graphene ، Application of finite element ، Graphene-based materials ، ۲D materials ، Mathematical Modeling